Question

I need help with Geometry

Answer 1

Answer:

The correct answer is:

Option 2: Yes, because the slopes of lines are negative reciprocals.

Step-by-step explanation:

Given equations of lines are:

Line p: x+2y=1

Line q: y=2x+1

We can determine if two lines are parallel or perpendicular by comparing the slopes of line.

Slope intercept form of line is given by the formula

$y = mx+b$

Equation of line q is already in slope intercept form.

We have to convert the equation of line p in slope-intercept form

$x+2y = 1\\2y = -x+1\\2y = -\frac{1}{2}x+\frac{1}{2}$

Slope of line p = 2

Slope of line q = -1/2

We can see that

$2.-\frac{1}{2} = -1$

The product of slopes of both lines is -1, hence, the lines are perpendicular.

Hence,

The correct answer is:

Option 2: Yes, because the slopes of lines are negative reciprocals.